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velocity potential for a rate formulation

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I have a question making me no sleep. In the elastic theory we have a separable Lagrangian L = T(v) + W(u) since we can write the internal elastic energy as a function of displacements. What happens if we use a rate form for the strain and the stress? Can we write the potential energy in terms of just velocities? If that is the case the stationary path of the Lagrangian reduces to:

 d/dt (dT/dv - dW/dv)  = 0

Joseph X. Zhou's picture

Ten commandments in systems biology

The 5th European Conference
on Complex System is holding in Dresden, Germany now. This is really
an emerging research area. The multiple para-sessions themselves show
how diverse and multi-disciplined it is. It includes:

  • Complex system method

  • Cognition

  • Networks

  • Social system

  • Biological system

Mai Lan NGUYEN's picture

Fracture energy for crack propagation in a 4 points bending notched beam

Hi everyone,

Anyone can tell me how to determine the fracture energy for crack propagation in a 4 points bending notched beam (mode I)?

Amit Acharya's picture

Musings on continuum thermodynamic formalism and (yet another) damage model

A technique for setting up generalized continuum theories based on a balance law and nonlocal thermodynamics is suggested. The methodology does not require the introduction of gradients of the internal variable in the free energy. Elements of a generalized damage model with porosity as the internal variable are developed as an example.

Amit Acharya's picture

New perspectives in plasticity theory


A field theory of dislocation mechanics and plasticity is illustrated through new results at the nano, meso, and macro scales. Specifically, dislocation nucleation, the occurrence of wave-type response in quasi-static plasticity, and a jump condition at material interfaces and its implications for analysis of deformation localization are discussed.

Derivatives of a volume integral with singular kernel

Hi everybody, 

In fact, I encounter this problem in my research and I would be grateful if someone can help. In micro mechanics, there are many problems concerning Green functions, e.g: the displacement is calculated from the distributed force in the domain, etc. Consider the following integral to determine the displacement field.

Zhiliang Zhang's picture

The one-million-dollar Kavli Prizes in Nanoscience, Neuroscience and Astrophysics call for nominations

The Kavli Prize – three international awards for outstanding contributions to the fields of nanoscience, neuroscience and astrophysics – will be awarded for the first time in 2008. The Kavli Foundation has established these international awards to recognize seminal advances in scientific research. Each prize will consist of a scroll, a medal and a cash award of USD 1 million.

The Prizes will be awarded at a ceremony in Oslo, Norway, Fred Kavli’s native country, every two years, beginning in 2008.

A strained film grown on a vicinal substrate: Steps bunch or not to bunch?

When a strained film is grown on a vicinal substrate, the steps advance like a train when the deposited atoms have sufficient mobility to reach the step edges. However, as the steps advance, the strain-induced force monopoles associated with the steps cause the steps to attract to each other (J. Tersoff, PRL 74, 4962, (1995)), resulting in a thermodynamic instability of the steps in the form of step bunching (J. Tersoff, et al., PRL 75, 2730 (1995)).

Joseph X. Zhou's picture

Manchester biophysics meeting --- DNA nanomachines

The 2-day conference of biophysics in Manchester had just finished recently. It is really a meeting with a tight schedule and lots of new stuffs.

The meeting took place in the new building of multi-decipline biocenter in Manchester University. One interesting speech was given by Prof. Andrew J. Turberfield 

from Oxford university. Recently his group focuses on build some small molecule machines using DNA as the building block. It is just like 

mirende3yue's picture

How to represent the fiber-reinforced hyperelastic part

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Hey guys,

I am right now doing a FEA on cervical spine, however, the annulus property is complex, and I need to represent it by a fiber-reinforced hyperelastic part, I tried a lot, but still are nowhere.

 Can anybody tell me how to assign some embeded layers with elastic rebar element to a solid part ?

Thanks a lot.

mirende3yue's picture

Embeded element

Does anybody know how to represent a fiber-reinforced annulus part: ground substance is hyperelastic with neo-hooke coefficient; fiber-reinforcement are elastic?




Has any body used comsol pde. please guide me through the basics of comsol methods.





Numerical integration of non-polynomial functions

Hello colleagues,

 Would anybody know good references on numerical integration of non-polynomial functions? It would be enough for me to obtain one-dimensional rules. Of course, it could have impact for XFEM applications, but for another, improved XFEM method that we are developing.

Note  that I am not talking about integrating singularities, but non-polynomial functions. Examples:




product of these.

Thanks for any help,



Damodara Reddy's picture

Any open source code to generate carbon nanotube cap?

Generation of open ends carbon nanotubes coordinates (atomic positions) is easy and the generation of cap for these carbon nanotubes is extremely difficult. Some of the half-fullerenes (C60, C240, C540…) fit as a cap for the armchair and zigzag nanotubes. NanotubeModeler  ( software generates the carbon nanotubes with cap but they are limited to few armchair and zigzag configurations.

Nanshu Lu's picture

Co-evolution of local thinning and debonding

A 1um-thick Cu film was deposited on Kapton 50HN substrate, with a thin Cr interlayer to improve adhesion. The specimen was in-situ annealed at 200oC for 30min after deposition.

This FIB image was taken after the specimen was uniaxially stretched to 50% and released.

nunziovitt's picture

PhD in Applied Mechanics

Hi, guys...

I am a Mechanical Engineer (newly graduated).

Can somebody tell me where I can find a very good PhD studentship in APPLIED MECHANICS (i.e. vibro-acoustics, control systems, vehicle dynamics, etc...) in Europe?

I'm getting crazy with that... I hope somebody can help me.



Mechanics associated with grain-boundary diffusion and sliding in polycrystals and its application to nanocrystals

As stated by Richard Vinci and Oliver Kraft in the announcement of 2008 Gordon Research Conference on Thin Film and Small-Scale Mechanical Behavior, there is a compelling need to understand the critical roles of different deformation mechanisms in structures with small characteristic dimensions, like nanocrystals and thin films. We have recently studied deformation behaviors in nanostructured materials and thin films with deformation mechanisms including grain-boundary diffusion, grain-boundary sliding, and grain-interior plasticity. Some interesting mechanical phenomena associated with heterogeneous grain-boundary properties are found and summarized here.

    Harold S. Park's picture

    Material Instability - Questions

    Hello All:

    I'm interested in learning more about material instability, for example the localization criterions of Hill (1962) and Rudnicki and Rice (1975).  I also am aware of work by Rice (1976), in which a perturbation is made to the displacement field in the form of a plane harmonic wave, resulting in a strong ellipticity instability condition that looks like Det(Q), where Q = c_ijkl + Sigma_jk, i.e. a competition between material softening and stress increase determines the instability.  Furthermore, this stability criterion is developed assuming an infinite body.

    Wei Hong's picture

    A theory of coupled diffusion and large deformation in polymeric gels

       A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel.  This paper formulates a theory of the coupled mass transport and large deformation.

    BoJing Zhu's picture

    HIEM to 3D Crack in FC-EMTE-MCs

    Hypersingular Integral Equation Method to 3D Crack in Fully Coupled Electromagnetothermoelastic Multiphase Composites


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